The Removal of Spurious Spectral Peaks From Autoregressive Models for Irregularly Sampled Data

Irregularly sampled data can be transformed into a special equidistant missing-data problem. The data are approximated then by multiple equidistant missing-data sets within the same time frame, resampled with a multishift slotted nearest neighbor method. This resampling uses a fraction of the resampling time step as slot width. A special autoregressive (AR) estimator for multiple data sets with missing observations has been developed for the estimation of the power spectral density of this resampled signal. The algorithm estimates AR models for increasing model orders from the data and automatically selects the best order for the data from a number of candidates. Further, that selected AR model is used to estimate moving average (MA) and combined autoregressive moving average (ARMA) models as possible candidates for the data. Unfortunately, equidistant resampling always causes shift bias due to the shift of the observation times to an equidistant grid. This bias is sometimes the cause of spurious AR poles at higher frequencies. Therefore, the selected AR model order can have spurious high-frequency poles, incompatible with the continuous-time character of the irregularly sampled signal. The elimination of those impossible poles produces a corrected spectrum that will generally be a better approximation of the true irregular spectrum.